Posted by **Kayleigh** on Wednesday, April 10, 2013 at 12:03pm.

Consider the functions

f(x)= 5x+4/x+3(This is a fraction) and

g(x)= 3x-4/5-x(This is a fraction)

a)Find f(g(x))

b)Find g(f(x))

c)Determine whether the functions f and g are inverses of each other.

- Consider the functions -
**Steve**, Wednesday, April 10, 2013 at 12:37pm
f(g) = (5g+4)/(g+3)

= (5(3x-4)/(5-x)+4) / ((3x-4)/(5-x)+3)

= x

g(f) = (3f-4)/(5-f)

= (3((5x+4)/(x+3))-4) / (5-((5x+4)/(x+3)))

= x

since f(g) = g(f) = x, they are inverses

- Consider the functions -
**Kayleigh**, Wednesday, April 10, 2013 at 12:44pm
What are the values that need to be excluded?

- Consider the functions -
**Steve**, Wednesday, April 10, 2013 at 12:53pm
whatever makes the denominator zero must be excluded, since division by zero is undefined.

So, for f(g), x=5 is not allowed, since g(5) is not defined. In addition, since f(-3) is not defined, any x where g(x) = -3 must also be excluded. Luckily, there is no such x.

Use similar reasoning for g(f).

- Consider the functions -
**Kayleigh**, Wednesday, April 10, 2013 at 12:56pm
So there are no values to be excluded?

- Consider the functions -
**Steve**, Wednesday, April 10, 2013 at 1:04pm
Read what I said. You have to exclude x=5 because g(5) is not defined. Therefore, f(g(5)) is also not defined.

## Answer This Question

## Related Questions

- College Algebra! help! - Consider the following functions f(x)= (7x+8)/(x+3) and...
- pre calculus - consider the functions f(x)=x^3-3 and g(x)=3 sqrt x+3: a. find f(...
- math - consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2: a. find f(g(x)) b...
- math-please I really need help!!!!! - Consider the functions f(x)=2x+8/x+6; g(x...
- Math - If the inverses of two functions are both functions, will the inverse of ...
- Algebra-Functions - Could you please check my answers and help me with two ...
- Algebra 2 - for the functions f(x) = 5x +50 and g(x) = 1/5x -10 evaluate both f(...
- math - for the given functions f and g, find the specified value of the ...
- Calculus - We're learning about different kinds of functions and I don't really ...
- Mat101 - 5. Which of the following are functions? The last two problems, i.e., b...

More Related Questions